Linear Combination of Vectors

If we start with two vectors, and that are not parallel to each other, we can write any other vector as a linear combination of and . We can think of our usual coordinate plane as being defined by vectors and . If we create a new plane, using and , it will be easy to see how we can use them to name other vectors. Click the box next to "Animate" to change the coordinate system. Write the following in terms of and :
Given that and , express each vector above in terms of and . To confirm your results, uncheck "Animate" and use the original coordinate grid.